Finite Group Databasebeta

← C3×#83506 #11884056

Subgroups — C3×#83506 #11884056

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#546C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C22×C3×#214C211yesmaximal, characteristic, complemented
4C3×D4×Dic6C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6C3×#5218C211yesmaximal, characteristic, complemented
7C3×#5060C211yesmaximal, characteristic, complemented
8C3×#5054C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#5050C211yesmaximal, characteristic, complemented
11C3×#5042C211yesmaximal, characteristic, complemented
12C3×#5040C211yesmaximal, characteristic, complemented
13C3×#5019C211yesmaximal, characteristic, complemented
14C3×#5018C211yesmaximal, characteristic, complemented
15C3×#5011C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#83506C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C32×#124C2211yescharacteristic
23C32×#123—21no—
24C32×C22⋊Q8C2211yescharacteristic
25C32×#121—21no—
26C32×#121C2211yescharacteristic
27C32×#120—21no—
28C32×C4×D4C2211yescharacteristic
29C32×C4×D4C2211yescharacteristic
30C2×C32×C22⋊C4—21no—
31C3×#951—24no—
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#216C2211yescharacteristic, complemented
34C2×C3×#216C2211yescharacteristic, complemented
35C3×D4×Dic3—21no—
36C2×C3×#214—24no—
37C2×C3×#214C2211yescharacteristic
38C2×C3×#214C2211yescharacteristic
39C2×C3×#214C2211yescharacteristic
40C2×C3×#214C2211yescharacteristic
41C2×C3×#214C2211yescharacteristic
42C2×C3×#214C2211yescharacteristic
43C3×#924C2211yescharacteristic
44C3×#924C2211yescharacteristic, complemented
45C2×C3×#208C2211yescharacteristic, complemented
46C22×C3×C3⋊C8C2211yescharacteristic
47C3×#888—21no—
48C3×#878—21no—
49C3×#878—21no—
50C3×#869C2211yescharacteristic, complemented
51C3×C4×Dic6C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×#830C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
62C3×#803C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—21no—
67C3×#546D311yescharacteristic
68C3×#546C2×C311yescharacteristic
69C2×#951C2×C311yescharacteristic, complemented
70C22×#214C2×C311yescharacteristic, complemented
71D4×Dic6C2×C311yescharacteristic, complemented
72C3×#497—31no—
73C3×#468—31no—
74C3×#467—31no—
75C3×#464—31no—
76C3×#461—31no—
77C3×#452—31no—
78C3×#451—31no—
79C3×#450—31no—
80C3×#448—31no—
81C3×#440—31no—
82C3×#435—31no—
83#5239C2×C311yescharacteristic, complemented
84#5218C2×C311yescharacteristic, complemented
85#5060C2×C311yescharacteristic, complemented
86#5054C2×C311yescharacteristic, complemented
87#5051C2×C311yescharacteristic, complemented
88#5050C2×C311yescharacteristic, complemented
89#5042C2×C311yescharacteristic, complemented
90#5040C2×C311yescharacteristic, complemented
91#5019C2×C311yescharacteristic, complemented
92#5018C2×C311yescharacteristic, complemented
93#5011C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—22no—
99C2×C32×D4—21no—
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4—41no—
103C2×C32×D4D411yescharacteristic
104C2×C32×D4C2311yescharacteristic
105C2×C32×D4C2311yescharacteristic
106C22×C32×C4—21no—
107C22×C32×C4—21no—
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—22no—
114C2×C3×Dic6—21no—
115C2×C3×Dic6—21no—
116C2×C3×Dic6—41no—
117C2×C3×Dic6—41no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×C4⋊C4—21no—
122C32×C4⋊C4D411yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C32×C22⋊C4—21no—
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C32×C22⋊C4—21no—
129C32×C22⋊C4D411yescharacteristic
130C32×C22⋊C4D411yescharacteristic
131C32×C42C2311yescharacteristic
132C3×#217—21no—
133C3×#217—21no—
134C3×#216—22no—
135C3×#216—22no—
136C3×#216—41no—
137C3×#214—22no—
138C3×#214—22no—
139C3×#214—22no—
140C3×#214—22no—
141C3×#214—41no—
142C3×#214D414yescomplemented
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—21no—
145C3×C4⋊Dic3C2311yescharacteristic
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C3×#208—22no—
151C2×C3×C3⋊C8—22no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156#3266—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C22×C311yescharacteristic
160C22×C3×Q8—31no—
161C22×C3×Q8—31no—
162C22×C3×D4—21no—
163C22×C3×D4C2×D311yescharacteristic
164C22×C3×D4C22×C311yescharacteristic
165C22×Dic6C22×C311yescharacteristic
166C22×Dic6C22×C311yescharacteristic, complemented
167C3×#137—64no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×Q16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—64no—
178C2×C3×M16—31no—
179C22×C3×C8—31no—
180C3×C4⋊Q8—31no—
181C3×C4⋊Q8—61no—
182C3×#124—21no—
183C3×#124C2×D311yescharacteristic
184C3×#124C22×C311yescharacteristic
185C3×#123—22no—
186C3×#123—21no—
187C3×#123—21no—
188C3×C22⋊Q8—21no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—31no—
191C3×C22⋊Q8—61no—
192C3×C22⋊Q8—61no—
193C3×C22⋊Q8C2×D311yescharacteristic
194C3×C22⋊Q8C22×C311yescharacteristic
195C3×#121—22no—
196C3×#121—21no—
197C3×#121—21no—
198C3×#121—21no—
199C3×#121C2×D311yescharacteristic
200C3×#121C22×C311yescharacteristic
201C3×#120—22no—
202C3×#120—21no—
203C3×#120—21no—
204C3×C4×Q8—31no—
205C3×C4×D4—21no—
206C3×C4×D4—21no—
207C3×C4×D4—61no—
208C3×C4×D4C2×D311yescharacteristic
209C3×C4×D4C2×D311yescharacteristic
210C3×C4×D4C22×C311yescharacteristic
211C3×C4×D4C22×C311yescharacteristic
212C2×C3×C22⋊C4—22no—
213C2×C3×C22⋊C4—21no—
214C2×C3×C22⋊C4—21no—
215#951—24no—
216C2×#216C22×C311yescharacteristic, complemented
217C2×#216C22×C311yescharacteristic, complemented
218C2×#216C22×C311yescharacteristic, complemented
219D4×Dic3—21no—
220C2×#214—24no—
221C2×#214C22×C311yescharacteristic
222C2×#214C22×C311yescharacteristic
223C2×#214C22×C311yescharacteristic
224C2×#214C22×C311yescharacteristic
225C2×#214C22×C311yescharacteristic
226C2×#214C22×C311yescharacteristic
227#924C22×C311yescharacteristic
228#924C22×C311yescharacteristic, complemented
229C2×#208C22×C311yescharacteristic, complemented
230C22×C3⋊C8C22×C311yescharacteristic
231#888—21no—
232#878—21no—
233#878—21no—
234#869C22×C311yescharacteristic, complemented
235C4×Dic6C22×C311yescharacteristic, complemented
236C3×#107—31no—
237C3×C4⋊C8—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#103—31no—
241C3×#103—31no—
242C3×#102—31no—
243C3×#102—31no—
244C3×C22⋊C8—31no—
245C3×C22⋊C8—31no—
246C3×#97—31no—
247#835C22×C311yescharacteristic, complemented
248#832C22×C311yescharacteristic
249#832C22×C311yescharacteristic
250#830C22×C311yescharacteristic
251#830C22×C311yescharacteristic, complemented
252#810C22×C311yescharacteristic, complemented
253#810C22×C311yescharacteristic, complemented
254#810C22×C311yescharacteristic, complemented
255#807C22×C311yescharacteristic, complemented
256C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
257#803C22×C311yescharacteristic, complemented
258C23×C32—21no—
259C23×C32—21no—
260C23×C32—42no—
261C23×C32—42no—
262C23×C32—81no—
263C23×C32C2×D411yescharacteristic
264C23×C32C2×D411yescharacteristic
265C32×Q8—21no—
266C32×Q8—21no—
267C32×D4—21no—
268C32×D4—22no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C32×D4—42no—
273C32×D4—81no—
274C32×D4C2×D412yes—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—42no—
282C2×C32×C4—81no—
283C2×C32×C4C2×D411yescharacteristic
284C2×C32×C4C2×D411yescharacteristic
285C2×C32×C4C2×D411yescharacteristic
286C2×C32×C4C2×D411yescharacteristic
287C2×C32×C4C2411yescharacteristic
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—42no—
293C2×C3×Dic3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3×Dic6—42no—
300C3×Dic6—42no—
301C3×Dic6C2×D412yes—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#137—31no—
307C22×SD16—31no—
308D4×Q8—31no—
309#546C3×D311yescharacteristic
310#497—31no—
311#468—31no—
312#467—31no—
313#464—31no—
314#461—31no—
315#452—31no—
316#451—31no—
317#450—31no—
318#448—31no—
319#440—31no—
320#435—31no—
321C24×C3—22no—
322C24×C3—21no—
323C24×C3—21no—
324C3×#41—22no—
325C3×#41—22no—
326C3×#41—42no—
327C3×#41—41no—
328C3×#41—41no—
329C3×#41—42no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—31no—
333C2×C3×Q8—31no—
334C2×C3×Q8—62no—
335C2×C3×Q8—62no—
336C2×C3×Q8—61no—
337C2×C3×Q8—61no—
338C2×C3×Q8—121no—
339C2×C3×Q8—121no—
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×Q8C23×C311yescharacteristic
342C2×C3×D4—22no—
343C2×C3×D4—22no—
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—22no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—21no—
353C2×C3×D4—21no—
354C2×C3×D4—21no—
355C2×C3×D4—21no—
356C2×C3×D4—42no—
357C2×C3×D4—41no—
358C2×C3×D4—41no—
359C2×C3×D4—42no—
360C2×C3×D4#6711yescharacteristic
361C2×C3×D4C3×D411yescharacteristic
362C2×C3×D4C22×D311yescharacteristic
363C2×C3×D4C22×D311yescharacteristic
364C2×C3×D4C23×C311yescharacteristic
365C2×C3×D4C23×C311yescharacteristic
366C22×C3×C4—22no—
367C22×C3×C4—22no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C23×C311yescharacteristic
379C22×C3×C4C23×C311yescharacteristic
380C22×Dic3—21no—
381C22×Dic3—21no—
382C2×Dic6—22no—
383C2×Dic6—22no—
384C2×Dic6—21no—
385C2×Dic6—21no—
386C2×Dic6—41no—
387C2×Dic6—41no—
388C2×Dic6C23×C311yescharacteristic
389C2×Dic6C23×C311yescharacteristic
390C2×Dic6C23×C311yescharacteristic
391C3×Q16—62no—
392C3×Q16—62no—
393C3×Q16—121no—
394C3×SD16—34no—
395C3×SD16—62no—
396C3×SD16—62no—
397C3×SD16—62no—
398C3×SD16—62no—
399C3×SD16—121no—
400C3×M16—62no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—31no—
405C2×C3×C8—62no—
406C3×C4⋊C4—22no—
407C3×C4⋊C4—21no—
408C3×C4⋊C4—21no—
409C3×C4⋊C4—21no—
410C3×C4⋊C4—21no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4—61no—
414C3×C4⋊C4—61no—
415C3×C4⋊C4—61no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4#6711yescharacteristic
418C3×C4⋊C4C3×D411yescharacteristic
419C3×C4⋊C4C22×D311yescharacteristic
420C3×C4⋊C4C23×C311yescharacteristic
421C3×C22⋊C4—22no—
422C3×C22⋊C4—22no—
423C3×C22⋊C4—22no—
424C3×C22⋊C4—22no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—21no—
427C3×C22⋊C4—21no—
428C3×C22⋊C4—21no—
429C3×C22⋊C4—21no—
430C3×C22⋊C4—21no—
431C3×C22⋊C4—21no—
432C3×C22⋊C4—21no—
433C3×C22⋊C4—21no—
434C3×C22⋊C4—21no—
435C3×C22⋊C4—21no—
436C3×C22⋊C4—21no—
437C3×C22⋊C4—21no—
438C3×C22⋊C4—61no—
439C3×C22⋊C4—61no—
440C3×C22⋊C4#6711yescharacteristic
441C3×C22⋊C4#6711yescharacteristic
442C3×C22⋊C4C3×D411yescharacteristic
443C3×C22⋊C4C3×D411yescharacteristic
444C3×C42—21no—
445C3×C42—61no—
446C3×C42C22×D311yescharacteristic
447C3×C42C23×C311yescharacteristic
448#217—21no—
449#217—21no—
450#216—22no—
451#216—22no—
452#216—41no—
453#214—22no—
454#214—22no—
455#214—22no—
456#214—22no—
457#214—41no—
458#214C3×D414yescomplemented
459C4⋊Dic3—21no—
460C4⋊Dic3—21no—
461C4⋊Dic3C23×C311yescharacteristic
462Dic3⋊C4—21no—
463Dic3⋊C4—21no—
464Dic3⋊C4—21no—
465C4×Dic3—21no—
466#208—22no—
467C2×C3⋊C8—22no—
468C2×C3⋊C8C23×C311yescharacteristic
469C2×C3⋊C8C23×C311yescharacteristic
470C2×C3⋊C8C23×C311yescharacteristic
471C2×C3⋊C8C23×C311yescharacteristic
472C22×C32—22no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—84no—
484C22×C32#13712yescomplemented
485C22×C32C22×D411yescharacteristic
486C32×C4—21no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4—41no—
491C32×C4—41no—
492C32×C4C22×D411yescharacteristic
493C32×C4H(5,𝔽2)11yescharacteristic
494C3×Dic3—22no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C2×#41C2×C3×D311yescharacteristic
499C22×Q8—31no—
500C22×Q8—31no—
501C22×D4C2×C3×D311yescharacteristic
502#137—64no—
503C2×Q16—31no—
504C2×Q16—31no—
505C2×Q16—31no—
506C2×SD16—31no—
507C2×SD16—31no—
508C2×SD16—31no—
509C2×SD16—31no—
510C2×SD16—31no—
511C2×SD16—31no—
512C2×SD16—64no—
513C2×M16—31no—
514C22×C8—31no—
515C4⋊Q8—31no—
516C4⋊Q8—61no—
517#124C2×C3×D311yescharacteristic
518#123—21no—
519C22⋊Q8—31no—
520C22⋊Q8—31no—
521C22⋊Q8—61no—
522C22⋊Q8—61no—
523C22⋊Q8C2×C3×D311yescharacteristic
524#121—21no—
525#121C2×C3×D311yescharacteristic
526#120—21no—
527C4×Q8—31no—
528C4×D4—61no—
529C4×D4C2×C3×D311yescharacteristic
530C4×D4C2×C3×D311yescharacteristic
531C2×C22⋊C4—21no—
532#107—31no—
533C4⋊C8—31no—
534#103—31no—
535#103—31no—
536#103—31no—
537#103—31no—
538#102—31no—
539#102—31no—
540C22⋊C8—31no—
541C22⋊C8—31no—
542#97—31no—
543C23×C3—22no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—22no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3—44no—
554C23×C3—44no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3—81no—
558C23×C3—81no—
559C23×C3—82no—
560C23×C3C2×#6711yescharacteristic
561C23×C3C2×#6711yescharacteristic
562C23×C3C2×C3×D411yescharacteristic
563C23×C3C2×C3×D411yescharacteristic
564C3×Q8—21no—
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—32no—
569C3×Q8—41no—
570C3×Q8—41no—
571C3×Q8—61no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×Q8—61no—
575C3×Q8—61no—
576C3×Q8—122no—
577C3×Q8—122no—
578C3×D4—22no—
579C3×D4—22no—
580C3×D4—22no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—22no—
588C3×D4—41no—
589C3×D4—41no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—42no—
593C3×D4—42no—
594C3×D4—42no—
595C3×D4—44no—
596C3×D4—44no—
597C3×D4—81no—
598C3×D4—81no—
599C3×D4—82no—
600C3×D4D3×D412yes—
601C3×D4C2×C3×D412yes—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—42no—
626C2×C3×C4—42no—
627C2×C3×C4—44no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—81no—
633C2×C3×C4—81no—
634C2×C3×C4—82no—
635C2×C3×C4—122no—
636C2×C3×C4—122no—
637C2×C3×C4C2×#6711yescharacteristic
638C2×C3×C4C2×#6711yescharacteristic
639C2×C3×C4C2×#6711yescharacteristic
640C2×C3×C4C2×#6711yescharacteristic
641C2×C3×C4C2×C3×D411yescharacteristic
642C2×C3×C4C2×C3×D411yescharacteristic
643C2×C3×C4C2×C3×D411yescharacteristic
644C2×C3×C4C2×C3×D411yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C24×C311yescharacteristic
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—42no—
652C2×Dic3—42no—
653Dic6—21no—
654Dic6—21no—
655Dic6—21no—
656Dic6—21no—
657Dic6—21no—
658Dic6—42no—
659Dic6—42no—
660Dic6C2×C3×D412yes—
661C3×C8—32no—
662C3×C8—61no—
663C3×C8—61no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—21no—
667C3⋊C8—21no—
668C3⋊C8C2×C3×D412yes—
669C2×C32—22no—
670C2×C32—42no—
671C2×C32—41no—
672C2×C32—81no—
673C2×C32D4211yescharacteristic
674C2×C32C2×#13711yescharacteristic
675C2×C32#57711yescharacteristic
676C24—21no—
677#41—22no—
678#41—41no—
679C2×Q8—31no—
680C2×Q8—31no—
681C2×Q8—31no—
682C2×Q8—62no—
683C2×Q8—62no—
684C2×Q8—61no—
685C2×Q8—61no—
686C2×Q8—121no—
687C2×Q8—121no—
688C2×Q8C22×C3×D311yescharacteristic
689C2×D4—22no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—41no—
694C2×D4C3×#6711yescharacteristic
695C2×D4C22×C3×D311yescharacteristic
696C2×D4C22×C3×D311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4C22×C3×D311yescharacteristic
702C22×C4C22×C3×D311yescharacteristic
703Q16—62no—
704Q16—62no—
705Q16—121no—
706SD16—34no—
707SD16—62no—
708SD16—62no—
709SD16—62no—
710SD16—62no—
711SD16—121no—
712M16—62no—
713C2×C8—31no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—62no—
718C4⋊C4—21no—
719C4⋊C4—31no—
720C4⋊C4—61no—
721C4⋊C4—61no—
722C4⋊C4—61no—
723C4⋊C4—61no—
724C4⋊C4—61no—
725C4⋊C4C3×#6711yescharacteristic
726C4⋊C4C22×C3×D311yescharacteristic
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4C3×#6711yescharacteristic
735C22⋊C4C3×#6711yescharacteristic
736C42—61no—
737C42C22×C3×D311yescharacteristic
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—24no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—21no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—84no—
774C22×C3—84no—
775C22×C3—88no—
776C22×C3#95112yescomplemented
777C22×C3C3×#13712yescomplemented
778C22×C3C22×#6711yescharacteristic
779C22×C3C22×C3×D411yescharacteristic
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—62no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4—121no—
804C3×C4C2×D3×D411yescharacteristic
805C3×C4#100411yescharacteristic
806C3×C4C22×C3×D411yescharacteristic
807C3×C4C3×H(5,𝔽2)11yescharacteristic
808Dic3—22no—
809Dic3—41no—
810Dic3—41no—
811Dic3—41no—
812C32#326611yescharacteristic, complemented, Sylow
813C23—21no—
814C23—21no—
815C23—42no—
816C23—42no—
817C23—81no—
818C23C2×C3×#6711yescharacteristic
819C23C2×C3×#6711yescharacteristic
820Q8—21no—
821Q8—21no—
822Q8—32no—
823Q8—61no—
824Q8—61no—
825Q8—61no—
826Q8—61no—
827Q8—61no—
828Q8—122no—
829Q8—122no—
830D4—22no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—42no—
835D4—42no—
836D4—81no—
837D4C3×D3×D412yes—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—42no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—81no—
850C2×C4—122no—
851C2×C4—122no—
852C2×C4C2×C3×#6711yescharacteristic
853C2×C4C2×C3×#6711yescharacteristic
854C2×C4C2×C3×#6711yescharacteristic
855C2×C4C2×C3×#6711yescharacteristic
856C2×C4C23×C3×D311yescharacteristic
857C8—32no—
858C8—61no—
859C8—61no—
860C8—61no—
861C2×C3—22no—
862C2×C3—22no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—44no—
868C2×C3—41no—
869C2×C3—42no—
870C2×C3—41no—
871C2×C3—42no—
872C2×C3—81no—
873C2×C3—82no—
874C2×C3—81no—
875C2×C3—81no—
876C2×C3D4×#6711yescharacteristic
877C2×C3C2×#95111yescharacteristic
878C2×C3#583611yescharacteristic
879C2×C3C3×D4211yescharacteristic
880C2×C3C2×C3×#13711yescharacteristic
881C2×C3C3×#57711yescharacteristic
882C22—21no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—84no—
894C22C3×#95112yescomplemented
895C22C22×C3×#6711yescharacteristic
896C4—21no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—41no—
901C4—41no—
902C4—62no—
903C4—121no—
904C4—121no—
905C4—121no—
906C4C2×C3×D3×D411yescharacteristic
907C4C3×#100411yescharacteristic
908C3—21no—
909C3#8350611yescharacteristic, direct product factor
910C3C3×#326611yescharacteristic, complemented
911C2—22no—
912C2—41no—
913C2—42no—
914C2—81no—
915C2C3×D4×#6711yescharacteristic
916C2C2×C3×#95111yescharacteristic
917C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#546C2
socleC22×C32C22×D4
hypercenterC3×#546D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C22×C3×#214C2semidirect
4. C3×D4×Dic6C2semidirect
5. C3×#5239C2semidirect
6. C3×#5218C2semidirect
7. C3×#5060C2semidirect
8. C3×#5054C2semidirect
9. C3×#5051C2semidirect
10. C3×#5050C2semidirect
11. C3×#5042C2semidirect
12. C3×#5040C2semidirect
13. C3×#5019C2semidirect
14. C3×#5018C2semidirect
15. C3×#5011C2semidirect
17. #83506C3direct (N × H)
21. C22×C3×Dic6C22semidirect
32. C2×C3×#216C22semidirect
33. C2×C3×#216C22semidirect
34. C2×C3×#216C22semidirect
44. C3×#924C22semidirect
45. C2×C3×#208C22semidirect
50. C3×#869C22semidirect
51. C3×C4×Dic6C22semidirect
52. C3×#835C22semidirect
56. C3×#830C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
59. C3×#810C22semidirect
60. C3×#807C22semidirect
61. C3×C4⋊(C3⋊C8)C22semidirect
62. C3×#803C22semidirect
69. C2×#951C2×C3semidirect
70. C22×#214C2×C3semidirect
71. D4×Dic6C2×C3semidirect
83. #5239C2×C3semidirect
84. #5218C2×C3semidirect
85. #5060C2×C3semidirect
86. #5054C2×C3semidirect
87. #5051C2×C3semidirect
88. #5050C2×C3semidirect
89. #5042C2×C3semidirect
90. #5040C2×C3semidirect
91. #5019C2×C3semidirect
92. #5018C2×C3semidirect
93. #5011C2×C3semidirect
142. C3×#214D4semidirect
166. C22×Dic6C22×C3semidirect
216. C2×#216C22×C3semidirect
217. C2×#216C22×C3semidirect
218. C2×#216C22×C3semidirect
228. #924C22×C3semidirect
229. C2×#208C22×C3semidirect
234. #869C22×C3semidirect
235. C4×Dic6C22×C3semidirect
247. #835C22×C3semidirect
251. #830C22×C3semidirect
252. #810C22×C3semidirect
253. #810C22×C3semidirect
254. #810C22×C3semidirect
255. #807C22×C3semidirect
256. C4⋊(C3⋊C8)C22×C3semidirect
257. #803C22×C3semidirect
458. #214C3×D4semidirect
484. C22×C32#137semidirect
776. C22×C3#951semidirect
777. C22×C3C3×#137semidirect
812. C32#3266semidirect
894. C22C3×#951semidirect
909. C3#83506direct (N × H)
910. C3C3×#3266semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#5462
C2×C3×#9512
C22×C3×#2142
C3×D4×Dic62
C3×#52392
C3×#52182
C3×#50602
C3×#50542
C3×#50512
C3×#50502
C3×#50422
C3×#50402
C3×#50192
C3×#50182
C3×#50112
C3×#32663
#835063